Rs. Maier et Dl. Stein, ESCAPE PROBLEM FOR IRREVERSIBLE SYSTEMS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 48(2), 1993, pp. 931-938
The problem of noise-induced escape from a metastable state arises in
physics, chemistry, biology, systems engineering, and other areas. The
problem is well understood when the underlying dynamics of the system
obey detailed balance. When this assumption fails many of the results
of classical transition-rate theory no longer apply, and no general m
ethod exists for computing the weak-noise asymptotic behavior of funda
mental quantities such as the mean escape time. In this paper we prese
nt a general technique for analyzing the weak-noise limit of a wide ra
nge of stochastically perturbed continuous-time nonlinear dynamical sy
stems. We simplify the original problem, which involves solving a part
ial differential equation, into one in which only ordinary differentia
l equations need be solved. This allows us to resolve some old issues
for the case when detailed balance holds. When it does not hold, we sh
ow how the formula for the asymptotic behavior of the mean escape time
depends on the dynamics of the system along the most probable escape
path. We also present results on short-time behavior and discuss the p
ossibility of focusing along the escape path.